Lesson 2.5 Angle Relationships Geometry Chapter 2 Lesson 2.5 Angle Relationships

Linear Pair Conjecture C-1 If two angles form a linear pair, then the measure of the angles add up to 180 degrees. .

Vertical Angles Conjecture C-2 If two angles are vertical angles, then they have equal measures (are congruent). 2 Measure of angle 1 equals the measure of angle ______. While the Measure of angle 2 equals the measure of angle ______. 3 1 4

Putting C-1 and C-2 Together Example Problems: Solve for the missing variables. Solution: x + 130 = 180 (C-1) -130 -130 x = 50 **Use C-2 to solve for y and z. x z y Solution: 48 + a + 46 = 180 (Conjecture???) a + 94 = 180 - 94 - 94 a = 86 **Use C-2 to solve for b,c,and d. a b c d

LESSON 2.6 SPECIAL ANGLES ON PARALLEL LINES CHAPTER 2 LESSON 2.6 SPECIAL ANGLES ON PARALLEL LINES

PARALLEL LINES CONJECTURE C-3 If two parallel lines are cut by a transversal, then corresponding angles are… alternate interior angles are… and alternate exterior angles are… CONGRUENT, CONGRUENT, CONGRUENT. KEY: Lines must be proven parallel.

Corresponding Angles Conjecture C-3a (CA Conjecture) If two parallel lines are cut by a transversal, then corresponding angles are ____________ CONGRUENT. 1 2 Angle 1 is congruent to angle 2. They are corresponding angles. 52 degrees Therefore, if angle 1 is 52 degrees, then angle 2 is __________.

Alternate Interior Angles Conjecture C-3b (AIA Conjecture) If two parallel lines are cut by a transversal, then alternate interior angles are _____________. CONGRUENT a b 3 c 4 d e f Use the AIA conjecture to determine which angle is congruent to angle c??? Angle 3 is congruent to angle 4. They are alternate interior angles. Answer: angle d

Alternate Exterior Angles Conjecture C-3c (AEA Conjecture) If two parallel lines are cut by a transversal, then alternate exterior angles are _____________. CONGRUENT According to the AEA conjecture, list all congruent angles. A B C D E F G H Answer: Angle A and Angle H Angle B and Angle G

CONVERSE OF THE PARALLEL LINES CONJECTURE C-4 If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, or congruent alternate exterior angles, then the lines are……………………………. PARALLEL

HOMEWORK Page 124; #1-6 Page 131; #1-7, 9,10, 14-16